Editing Schwinger function (section)

=== Cluster property ===

Cluster property (E4) says that Schwinger function <math>S_{p+q}</math> reduces to the product <math>S_{p}S_q</math> if two groups of points are separated from each other by a large constant translation:

:<math>\lim_{b\to \infty} S_{p+q}(x_1,\ldots,x_p,x_{p+1}+b,\ldots, x_{p+q}+b)
=S_{p}(x_1,\ldots,x_p) S_q(x_{p+1},\ldots, x_{p+q})</math>.

The limit is understood in the sense of distributions. There is also a technical assumption that the two groups of points lie on two sides of the <math>x^0=0</math> hyperplane, while the vector <math>b</math> is parallel to it:

:<math>x^0_1,\ldots,x^0_p>0,\quad x^0_{p+1},\ldots,x^0_{p+q}<0,\quad b^0=0.</math>